Your voice like any other area of your body needs to be conditioned. You can't jump into weight lifting full on everyday. At first, you need to start very slowly, a little but each day, and slowly adding to it. It's the same with growling. To prepare for a tour, or several shows in a row, if I have not growled in a couple weeks, my voice will be shot after the second show. For a couple weeks prior, you need to do it everyday, starting out with very little, and by the second week, running through the entire set daily. Again, it's also taking care of the throat during that time as well. Hot tea, honey, etc...
The coughing can be caused by a "Tickle". You'll get that when you voice starts to tear. It's the sure sign your voice is not conditioned for it, and you over did it. The "vomit pushes" may be a gag reflex from the tickle.
No one can tell you how to sound like Arkerfeldt, or Swano, or even me. It's just like "normal" singing. No one will sound exactly alike, and ou'll just sound like "you." There's no trick to sounding like someone, just work on your own voice, and make it sound the best it can. The only hint I can pass along, and what worked well for me over the years, is be as audible, and pronounce the words as clearly as you can. You'll find you may need to pronounce words differently while growling than speaking. Some accents need to be placed on different sounds to make it more audible.
It always pisses me off when people assume growling is "easy" just because it's not as technical as normal singing. Anyone can growl for a few seconds, but try it for 10, 20 or even 50 days in a row, and see if you can do it. Hell, lock yourself into a studio, and try to do an entire album in a weekend or 3 days with 10 hour sessions. It's far from easy to keep the "quality" of the growl for a good length of time. That's where the challenge comes in. I'm pretty sure Dan would agree. Dan, i'd love to hear your thoughts on this.